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Chapter 7 Risk and Real Options in Capital Budgeting

Chapter 7 Risk and Real Options in Capital Budgeting. Quantifying Risk and its Appraisal. Risk is the variability of possible outcomes Assumption of independence No causative relationship between cash flows from period to period Risk-free rate for discounting Isolate the time value of money

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Chapter 7 Risk and Real Options in Capital Budgeting

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  1. Chapter 7Risk and Real Options in Capital Budgeting

  2. Quantifying Risk and its Appraisal • Risk is the variability of possible outcomes • Assumption of independence • No causative relationship between cash flows from period to period • Risk-free rate for discounting • Isolate the time value of money • Standard deviation of the probability distribution of NPVs

  3. Standardizing the Dispersion • Assess the probability of adversity • Determining probabilities of adverse events • Consult the normal probability distribution table • Express differences from the mean in terms of standard deviations to determine the probability • Fundamental for a realistic assessment

  4. Information Generated • Probability distribution of IRR • Compute the mean and standard deviation • Nonnormal distribution • Biases in obtaining information • Adjustment for biases • Problems • Over-adjustment • Accountability • Results depends on behavioral considerations

  5. Dependence of Cash Flows (CFs) over Time • Consequence of CFs being correlated over time • Perfect correlation • CFs deviate in exactly the same relative manner • Linear function • Moderate correlation • Use a series of conditional probability distributions • Take account of the correlation of CFs over time

  6. Simulation • To approximate the standard deviation use random sampling • If CFs are highly correlated over time • The risk of a project will be greater than if they are mutually independent • Degree of dependence of CFs is important

  7. Total Risk for Multiple Investments • Total risk • The sum of systematic and unsystematic risk • Standard deviation (SD) • Correlation between projects • Feasible combinations and dominance

  8. Standard Deviation • Depends on • Degree of correlation between various projects • Higher the degree of positive correlation the greater the SD of the portfolio • SD of possible NPVs of each project • Greater the SD of individual projects the greater the SD of the portfolio

  9. Correlation Between Projects • Range of correlation • Between 0 and 1.00 • Lack of negatively correlated projects • Unrelated lines of business tend to have low degrees of correlation

  10. Feasible Combination and Dominance • Evaluating feasible combinations • Determine which combinations dominate in NPV and/or SD • Determines the efficient frontier • Relation to existing portfolio • Investment proposals can be eliminated because they are dominated

  11. Real Options in Capital Investments • Valuation in general • Types of option • Option to vary output • Option to abandon • Option to postpone

  12. Valuation in General • Real options • Enhance the worth of a project • Difficult to value • Decision trees • Simulations • Ad hoc approaches • Project worth = NPV + option value • As the number of options increases • Uncertainty increases • Option value increases • Project’s worth increases

  13. The Option to Expand • Using a decision tree • Expected NPVs for the various branches • Sequence of decisions and chance events • Optimal set of decisions • Rolling back the tree • Backward induction • Comparing NPVs • Optimal decision at the first decision point

  14. The Option to Abandon • Provides a safety net • Consists of • Selling the asset or • Employing the asset in another area

  15. Economic Rationale for Abandonment • Same as capital budgeting • Project worth = NPV without abandonment + Value of abandonment option • Abandon a project • If the PV of possible future benefits > current abandonment value • Appears better now than in the future

  16. Abandonment Option Makes Situation Better • A significant improvement occurs • A portion of the downside is eliminated when events turn unfavorable • Abandonment is more valuable • The greater the volatility of CFs • Abandonment mitigates the effects of bad outcomes • Ongoing Abandonment Evaluations • Optimal time to abandon • Continual assessment of projects

  17. The Option to Postpone or Time • Obtain new information • Market • Prices • Cost • Give up • Interim CFs • First mover advantage • Commodity situation • Noncommodity situation

  18. Final Observations on Real Options • Real options are different from financial options • Cannot use risk neutrality • Exercise price can change over time • Volatility is difficult to measure • Imprecise opportunity cost • More difficult to value • Recognition of management flexibility • More uncertainty is a positive with real options

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